ax+b=c(X+1)

Solution for ax+b=c(X+1) equation:

Simplifying
ax + b = c(X + 1)

Reorder the terms:
ax + b = c(1 + X)
ax + b = (1 * c + X * c)
ax + b = (1c + cX)

Solving
ax + b = 1c + cX

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
ax + b + -1b = 1c + -1b + cX

Combine like terms: b + -1b = 0
ax + 0 = 1c + -1b + cX
ax = 1c + -1b + cX

Reorder the terms:
ax = -1b + 1c + cX

Divide each side by 'x'.
a = -1bx-1 + cx-1 + cx-1X

Simplifying
a = -1bx-1 + cx-1 + cx-1X